17. The top of Trinity Church steeple in New York is 268 ft. from the ground; the height of the steeple above the church plus 12 ft. is equal to the height of the church. Find the height of the steeple above the church? 18. Two persons have the same income: A saves of his, but B by spending $300 a year more than A, at the end of 2 years is $200 in debt. What is their income?

19. Divide $2520 among 3 persons, so that the second shall have as much as the first, and the third as much as the other two. What is the share of each?

20. A man owes a debt to be paid in 4 equal installments of 4, 9, 12, and 20 months respectively; a discount of 5% being allowed, he finds that $1500 ready money will pay the debt. What is the amount of the debt ?

21. A quantity of flour is to be distributed among some poor families; if 50 lb. are given to each family, there will be 6 lb. left; if 51 lb. are given to each, there will be wanting 4 lb. What is the quantity of flour?

22. I have three notes payable as follows: one for $400, due Jan. 1, 1875; another for $700, due Sept. 1, 1875; and another for $1000, due April 1, 1876. What is the

average of maturity?

23. An estate worth $123251.82 is left to four sons, whose ages are 19, 17, 13, and 11 years, respectively, and is to be so divided that each part being put out at 7% simple interest, the amounts shall be equal when they become 21 years of age. What are the parts?

24. If a piece of silk cost $1.20 a yard, at what price must it be marked that it may be sold at 10% less than the marked price, and still make a profit of 20%?

25. A farmer sold 100 geese and turkeys; for the geese

he received $.75 apiece, and for the turkeys $1.25 apiece, and for the whole $104. What was the number of each?

26. A man left his property to three sons; to A wanting $180, to B, and to C the rest, which was $590 less than A and B received. What was the whole estate?

27. What is the simple interest and the amount; the compound interest and amount; the present worth and the true discount; the bank discount and the proceeds of $1920, for 2 yr. 5 mo. 12 da., at 6%? Also the face of the note, which when discounted at a bank for the same time, and at the same rate, will produce the same sum? 28. Divide $1500 among 3 persons, so that the share of the second may be greater than that of the first, and the share of the third greater than that of the second.

29. A merchant owes for three bills of goods as follows: $500 due March 1, $800 due June 1, and $600 due Aug. 1. He wishes to give two notes for the amount, one for $1000, payable April 1; what must be the face, and when the maturity, of the other?

30. A man in New York purchased a draft on Chicago for $10640, drawn at 60 da., $10302.18. What was the course of exchange?

31. B. B. Northrop, through his broker, invested a ⚫ certain sum in U. S. 6's, 5-20, at 107, and twice as much in U. S. 5's of '81, at 984, brokerage on each, 1%. His income from both investments is $1674. How much did he invest in each kind of stock?

32. A, B, and C are under a joint contract to furnish 6000 bu. of corn, at $.48 a bushel; A's corn is worth $.45, B's $.51, and C's $.54 ; how many bushels must each put into the mixture that the contract may be fulfilled?

33. A cask contains 42 U. S. gallons of wine, worth $44 per gallon. How much less will it cost in U. S. money, at the rate of £1 2s. per the Imperial gallon?

34. A garden 400 ft. long and 300 ft. wide has a walk 20 ft. wide laid off from each of its two sides. What is the ratio between the area of the walk and the area of what remains ?

35. A commission merchant in Charleston received into his store on May 1, 1875, 1000 bbl. of flour, paying as charges on the same day, freight $175.48, cartage $56.25, and cooperage $8.37. He sold out the shipment as follows: June 3, 200 bbl. @ $6.25; June 30, 350 bbl. @ $6.50 July 29, 400 bbl. @ $6.12; Aug. 6, 50 bbl. @ $6. Required, the net proceeds, and the date when they shall be accredited to the owner, allowing commission at 31%, and storage at 2 cents per week per bbl.

36. Three men engage in manufacturing. L puts in $3840 for 6 mo. ; M, a sum not specified for 12 mo.; and N, $2560 for a time not specified. L received $4800 for his capital and profits; M, $9600 for his; and N, $4160 for his. Required, M's capital and N's time.

37. My expenditures in building a house, in the year 1874, were as follows: Jan. 16, $536.78; Feb. 20, $425.36; March 4, $259.25; April 24, $786.36. At the last date I sold the house for exactly what it cost, interest at 6 per cent. on the money expended added, and took the purchaser's note for the amount. What was the face of

the note?

38. A man bought a farm for $6000, and agreed to pay principal and interest in 3 equal annual installments. What was the annual payment, interest being 6%?

793. 1. What is the product of 3 used twice as a factor?

2. What is the product of 3 used 3 times as factor . 3. What is the product of 4 used 3 times as a factor? 4. What is the result of using 5 twice as a factor? 5. What is the product of used twice as a factor?

6. What is the result of using twice as a factor? , three times as a factor?

7. What number will be produced by using .3 twice as a factor? .7, twice? .4, three times? .05, twice?

8. A room is 9 ft. on each side; how many square feet

in the floor?

9. A cubical block of stone is 4 ft. on each edge; how many cubic feet does it contain?

DEFINITIONS.

794. A Power of a number is the product of factors, each of which is equal to that number. Thus, 27 is the third power of 3, since 27 = 3 × 3 × 3.

795. Involution is the process of finding any power

of a number.

796. The Base or Root of a power is one of the equal factors of the power. Thus, 27 is the third power of 3, and 3 is the base, or root, of that power.

797. The Exponent of a power is a number placed at the right of the base and a little above it, to show how many times it is used as a factor to produce the power. It also denotes the degree of the power.

Thus,

83 = 3 x 3 x 3 = 27

799. The Cube of a number is its third power, so called because the number of units of volume in a cube is equal to the third power of the number of linear units in one of its edges.

800. A Perfect Power is a number which can be resolved into equal factors. Thus, 25 is a perfect power of the second degree, and 27 is a perfect power of the third degree.